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In 1935 at his annual birthday party/press meeting a 79-year-old Tesla
related a story where he claimed a version of his mechanical
oscillator caused extreme vibrations in structures and even an
earthquake in downtown New York City ... Tesla said the oscillator was around 7 inches (18 cm) long, and weighing one or two pounds; something "you could put
in your overcoat pocket". At one point while experimenting with the
oscillator, he alleged it generated a resonance in several buildings
causing complaints to the police. As the speed grew he said that the
machine oscillated at the resonance frequency of his own building and,
belatedly realizing the danger, he was forced to use a sledge hammer
to terminate the experiment.
https://en.wikipedia.org/wiki/Tesla%27s_oscillator

I am looking at ways to weaponize this machine.

(1) By creating an earthquake to disrupt attackers besieging one's camp/fortress.

(2) By focusing an Earthquake right through the Earth to destroy someone directly opposite (antipodean).

(3) Destroying a planet.

Question (EDITED)

Focusing for the moment on local effects:

Using technology up to the present era could we build and weaponize a vibration machine to create widespread destruction in an area of say a mile or two in diameter. This would be 'clean' in relation to nuclear or even conventional weapons. It could destroy buildings and infrastructure and disrupt enemy troops without lasting environmental effects.

The guys from Mythbusters once built a slightly larger version of Tesla's machine. They tested it on a bridge. Some vibration could be felt hundreds of feet away from the device, but that was that, and they called busted on the myth of the earthquake device.

Source: http://www.discovery.com/tv-shows/mythbusters/about-this-show/earthquake-machine/

Some people were quick to notice that the busters turned the device off after they started getting results, maybe for fear of the damage they could cause. More likely, though, is that Tesla's quake machine claims were exxagerated. The device works, it is just not as potent as advertised.

If you wish to cause an Earthquake proper, consider the amount of energy released by one. The formula goes like:

$$log_{10} E = 4.4 + 1.5M$$

Where $E$ is the energy quantity in joules, and $M$ is the magnitude in the Richter scale. Source: http://www.math.wichita.edu/~richardson/earthquake.html

From your description in the question you want a quake of magnitude of at least 7 in Richter. You'll need to put around 8 trillion joules under the city you wish to destroy in about a few seconds to a minute. Any device smaller than a city block storing that amount of energy would likely blow up. Back of napkin calculations seem to indicate it is close to a couple hundred kilotons of TNT, or about 15-20 Little Boy's (the atom bom dropped on Hiroshima).

I know a quake makes it seem like an Act of God, but the simple bombing alternative is looking more economic and feasible.

In response to an edit in the question, I have to raise two points:

1-) Please do not make edits that invalidate present answers.

2-) Buildings are generally not homogeneous enough that a single frequency or set of frequencies for mechanical waves would destroy them while sparing other things around them. If you wish to cause damage by vibrations, fly a fighter jet at low altitudes and watch as windows blow. You will also pop many eardrums in a very permanent manner. Some walls might crack, but don't expect any house to collapse.

Technically Tesla's device wouldn't create earthquakes but merely damage buildings similarly to the way earthquakes would.

Just a few days ago there was a goofy TV movie Bixler High Private Eye in which a contemporary teen discovers that his farther's high school science project a few decades ago had accidentally caused an earthquake and suspects that somebody has kidnapped his father and forced his father to cause mini earthquakes to demolish various buildings in the town.

It seems to me that if a real teenager accidentally invented an earthquake machine he wouldn't just ignore it for decades. Instead he would realize that if he could stumble across a way to make artificial earthquakes other kids doing science projects and scientists in laboratories would also do so sooner or later.

So he would go to the military and demonstrate his earthquake machine and tell them they would have to monitor all earthquakes around the world, no matter how small, to detect any that were artificial. And if they detected an artificial earthquake anywhere in the world, respond by creating an artificial earthquake in the same location, to show the makers of the earlier artificial earthquake that they weren't the first to invent earthquake machines and that there is someone capable of responding with earthquakes to any attack using earthquakes.

And that kid would probably work on the artificial earthquake project for his entire adult life.

What causes earthquakes? The planet Earth itself. There is an ocean of molten lava many miles down all around the Earth, and the solid surface of the Earth floats on it like pack ice in the Arctic Ocean. like the oceans of water, the ocean of lava has currents.

Those slow moving but incredibly powerful currents of lava push the sold rock above them slowly but surely with incredible force. There are places where one sheet of rock meets another and is forced below it, and cracks within each sheet of rock where the sheet is being twisted and torn.

So there are many fault lines where huge masses of rock are slowly sliding past each other. Horizontal fault lines, vertical fault lines, and diagonal fault lines. And sometimes the rock masses get stuck on projecting rocks or sticky lava or something and stop moving and the pressure builds up greater and greater and greater until something snaps and the rocks suddenly move a lot, causing an earthquake.

It has been claimed that many different types of human activities can cause earthquakes (mostly small earthquakes).

While most earthquakes are caused by movement of the Earth's tectonic plates, human activity can also produce earthquakes. Four main activities contribute to this phenomenon: storing large amounts of water behind a dam (and possibly building an extremely heavy building), drilling and injecting liquid into wells, and by coal mining and oil drilling.[43] Perhaps the best known example is the 2008 Sichuan earthquake in China's Sichuan Province in May; this tremor resulted in 69,227 fatalities and is the 19th deadliest earthquake of all time. The Zipingpu Dam is believed to have fluctuated the pressure of the fault 1,650 feet (503 m) away; this pressure probably increased the power of the earthquake and accelerated the rate of movement for the fault.[44]

The greatest earthquake in Australia's history is also claimed to be induced by human activity: Newcastle, Australia was built over a large sector of coal mining areas. The earthquake has been reported to be spawned from a fault that reactivated due to the millions of tonnes of rock removed in the mining process.[45]

https://en.wikipedia.org/wiki/Earthquake#Induced_seismicity1

There is an article and list of possibly human caused earthquakes, some of which caused major damage and many deaths.

https://en.wikipedia.org/wiki/Induced_seismicity2

Clearly if someone wanted to devastate his own country, he could spend countless billions of dollars on various large-scale projects that would increase the frequency and severity of earthquakes in his own country - probably only slightly.

But an artificial earthquake one could trigger at any moment one wanted in another country would be a different matter. It should be possible to cause an earthquake due to happen along a fault line to happen when one wants it to happen instead of just waiting for it to happen sometime in the future.

One would have to excavate hundreds or thousands of feet down in some spots, and a few miles in other spots, and tens of miles (many times deeper than humans have ever done before) in still other spots, to reach the fault line. And then place hundreds and thousands of nuclear weapons along the fault line.

If the nuclear bombs were exploded all at once they would vaporize many cubic miles of rock and liquify many other cubic miles of rock. And if - repeat if - one's scientific calculations were correct, that would lubricate the fault line enough and the rocks would suddenly slide past each other, causing the earthquake to happen when it was desired.

Of course there would be a few minor problems like keeping the biggest excavation project ever hidden from the enemy in the enemy's own lands and smuggling thousands of atomic bombs into the enemy's land. And using thousands of atomic bombs in the normal way would probably be much more efficient.

That is the easy way to create a earthquake when and where you want it.

The difficult way would be to find a large asteroid or comet, probably at least tens of kilometers or miles in diameter, and using incredible amounts of energy, change its orbit in a manner carefully calculated to strike Earth at the time and place you want to create a major earthquake.

That should definitely create a major earthquake when and where it strikes. Of course, that earthquake will seem minor compared to other effects of the impact that could possibly make humans and many other life forms extinct and would certainly cause more death and destruction worldwide than any other event in at least fifty million years.

Since technically Tesla's device wouldn't create earthquakes but merely damage buildings similarly to the way earthquakes would, it is possible that there may be ways to damage buildings similar to earthquake damage that are not as hard to achieve as creating actual earthquakes.